Answer:
72
Step-by-step explanation:
Multiply. Note that when you multiply two negative numbers, the answer will be positive.
Combine:
-12 * -6 = 12 * 6 = 72
72 is your answer.
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Answers:
The formula is [f(-1)-f(-4)]/[3]
The value of f(-1) is 3
The value of f(-4) is -3
The average rate of change is 2
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Explanation:
For the first blank, we use the formula
[ f(b) - f(a) ]/[ b - a ]
where 'a' and 'b' are the endpoints for the x interval
In this case, a = -4 and b = -1. When you plug those values into the formula above, you get...
[ f(b) - f(a) ]/[ b - a]
[ f(-1) - f(-4)]/[ -1 - (-4) ]
[ f(-1) - f(-4)]/[ -1+4 ]
[ f(-1) - f(-4)]/[ 3 ]
which is why the answer is choice C for the first blank
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To compute the value of f(-1), we draw a vertical line through -1 on the x axis. This vertical line crosses the diagonal function graph at the point (-1,3). The y value of this point is what we want. Plugging in x = -1 leads to y = 3. This is why f(-1) = 3
If you want, you can draw a horizontal line through (-1,3) and you'll see it touching 3 on the y axis.
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Follow similar steps as above to compute f(-4). Draw a vertical line through x = -4 on the x axis. Mark the point where the vertical line crosses the diagonal line. This point is (-4,-3). Optionally draw a horizontal line over til you hit the y axis and you'll find that y = -3 corresponds to x = -4
This is why f(-4) = -3
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We'll use the last three sections to compute the average rate of change. Everything combines together building up to this moment.
From the first part, we had the formula
[ f(b) - f(a) ]/[ b - a ]
[ f(-1) - f(-4)]/[ 3 ]
We can replace the "f(-1)" with 3 since we found that f(-1) = 3
Similarly, f(-4) = -3 so we can replace the "f(-4)" with -3
Doing those replacements and simplifying leads to...
[ f(-1) - f(-4)]/[ 3 ]
[ 3 - (-3)]/[ 3 ]
[ 3 + 3]/[ 3 ]
6/3
2
So the average rate of change is 2
Note: because the entire graph is a straight line, the average rate of change for any interval a < x < b is going to be equal to the slope m. In this case, the slope of the line is m = 2/1 = 2. We move up 2 units each time we move to the right 1 unit along the diagonal line.
Area = length x width
96 = length x 8
Length =96/8
Length = 12 metres
I'm assuming you're referring to problem 6. You are asked to find the number of x intercepts or roots, which is another term for "zero". I prefer the term root or x intercept as "zero" seems misleading. Anyways, all we do is count the number of times the graph crosses the x axis. This happens 4 times as shown in the attached image below. I have marked these points in red. The graph can directly cross over the x axis, or it can touch the x axis and then bounce back. Either way, it is considered an x intercept.
<h3>Answer: there are 4 x intercepts (or 4 roots)</h3>
